How to solve 5x - 3y equals 0 to determine if x and y show direct variation?
5x - 3y = 0
5x = 3y or 3y = 5x
y = (5/3)x , which is in the form of y = mx, a direct variation.
To determine if the equation 5x - 3y = 0 represents direct variation between x and y, you can follow these steps:
Step 1: Rewrite the equation in the form y = kx.
Direct variation equations have the form y = kx, where k represents the constant of variation.
Given equation: 5x - 3y = 0
Rearrange the equation to isolate y:
-3y = -5x
Divide both sides of the equation by -3 to solve for y:
y = (5/3)x
Step 2: Compare the equation to y = kx.
Now that the equation is in the form y = kx, compare it to the general equation for direct variation. If they have the same form, it indicates that x and y show direct variation.
In this case, the equation y = (5/3)x matches the form y = kx, where k = 5/3. Therefore, x and y show direct variation.
To summarize, to determine if x and y show direct variation, you need to rewrite the given equation 5x - 3y = 0 in the form y = kx and compare it to the general equation for direct variation (y = kx). If they have the same form, x and y show direct variation.